First space cohomology of the orthosymplectic Lie superalgebra osp(3 vertical bar 2) in the Lie superalgebra of superpseudodifferential operators

摘要

We investigate the first cohomology space associated with the embedding of the Lie Orthosymplectic superalgebra osp(3 vertical bar 2) on the (1,3)-dimensional superspace R-1 vertical bar 3 in the Lie superalgebra S psi DO(3) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we give explicit expressions of the basis cocycles.